RESEARCH ARTICLE

Improving Species Distribution Modelling of

freshwater invasive species for management

applications

Marta Rodrıguez-ReyID*, Sofia Consuegra, Luca Borger, Carlos Garcia de Leaniz

Department of Biosciences, Swansea University, Swansea, United Kingdom

* marta.rodriguez.rey@gmail.com

Abstract

Freshwater ecosystems rank among the most endangered ecosystems in the world and are

under increasing threat from aquatic invasive species (AIS). Understanding the range

expansion of AIS is key for mitigating their impacts. Most approaches rely on Species Distri-

bution Models (SDMs) to predict the expansion of AIS, using mainly environmental vari-

ables, yet ignore the role of human activities in favouring the introduction and range

expansion of AIS. In this study, we use five SDM algorithms (independently and in ensem-

ble) and two accuracy measures (TSS, AUC), combined with a null modelling approach, to

assess the predictive performance of the models and to quantify which predictors (environ-

mental and anthropogenic from the native and introduced regions) best explain the distribu-

tion of nine freshwater invasive species (including fish, arthropods, molluscs, amphibians

and reptiles) in a large island (Great Britain), and which species characteristics affect model

performance. Our results show that the distribution of invasive species is difficult to predict

by SDMs, even in cases when TSS and AUC model accuracy values are high. Our study

strongly advocates the use of null models for testing SDMs performance and the inclusion of

information from the native area and a variety of both human-related and environmental pre-

dictors for a more accurate modelling of the range expansion of AIS. Otherwise, models that

only include climatic variables, or rely only on standard accuracy measures or a single algo-

rithm, might result in mismanagement of AIS.

Introduction

Developing a scientific basis for monitoring and managing invasive species and implementing

measures to manage pathways to prevent introductions is one of the CBD Aichi Targets for

2020 [1]. Freshwater invasions are of special concern, as freshwater ecosystems are among the

most diverse and endangered ecosystems in the world [2], harbouring more than a quarter of

all freshwater fauna threatened or recently extinct [3], in part due to the impact of non-native

freshwater species on native biodiversity [4]. Despite an increase in the number of studies

focusing on freshwater invasions in recent years [5], the main drivers of the introduction and

spread of aquatic invasive species (AIS) are still unknown [6].

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OPEN ACCESS

Citation: Rodrıguez-Rey M, Consuegra S, Borger L,

Garcia de Leaniz C (2019) Improving Species

Distribution Modelling of freshwater invasive

species for management applications. PLoS ONE

14(6): e0217896. https://doi.org/10.1371/journal.

pone.0217896

Editor: Paulo De Marco Junior, Universidade

Federal de Goias, BRAZIL

Received: May 30, 2018

Accepted: May 21, 2019

Published: June 17, 2019

Copyright: © 2019 Rodrıguez-Rey et al. This is an

open access article distributed under the terms of

the Creative Commons Attribution License, which

permits unrestricted use, distribution, and

reproduction in any medium, provided the original

author and source are credited.

Data Availability Statement: All relevant data used

in this investigation are available through the open

electronic sources cited within the paper and in

Table 1.

Funding: Funding for the study was provided by

the European Commission through a Marie

Sklodowska-Curie ITN (AQUAINVAD-ED; Grant

agreement no 642197). The funder had no role in

study design, data collection and analysis, decision

to publish, or preparation of the manuscript.

Species Distribution Models (SDMs) have widely been used as a management tool for AIS

[7]. These correlative techniques allow to model the distribution of species and map the spatial

suitability of areas based on the identification of statistical associations between species’ occur-

rence and predictor variables [8]. SDM outputs can be used for predicting changes in species’

distributions under environmental change and devise conservation and management strate-

gies [9]. Recent studies using SDMs have generated estimates of habitat suitability for AIS

mainly using environmental variables [7], based on the assumption of a natural colonisation

pattern, whereby species increase their range in areas with favourable environmental condi-

tions. This approach, using only climatic variables, has allowed the development of models for

forecasting invasive species’ distributions under future scenarios of climate change [10]. How-

ever, human-mediated range-shifts, although less predictable, may play a larger role than cli-

mate change in driving the expansion of AIS [11].

Human-related factors play indeed a fundamental role in the introduction and dispersal of

invasive species [12, 13], and accordingly, consideration of human mediated dispersion

appears essential for improving the explanatory and predictive accuracy of models [14]. Exist-

ing SDMs studies have incorporated variables such as human population density or presence

of roads [15] to account for the effect of human-mediated dispersal, but more detailed human-

related variables are required to account for propagule pressure (e.g. aquaculture, horticulture,

shipping frequency) [16].

Here, we assessed the relative ability of human-mediated and environmental predictors to

model the invasion of nine AIS belonging to five broad taxa (molluscs, arthropods, fish,

amphibians, and reptiles) in Great Britain, as a case study. We included environmental vari-

ables from both the native and invaded ranges of the species (to predict their potential eco-

physiological range) and human-related variables (to predict their human-induced geographi-

cal range), and tested model performance in relation to: (i) type of predictors (environmental

in the native and invaded region, environmental only in the invaded region or environmental

and anthropic in the invaded region) and (ii) characteristics of the species’ spatial records and

their invasion (e.g., time since first introduction, economic interest, distance between the

southernmost and northernmost records).

To test the predictive ability of the different models, our approach differs from similar stud-

ies on invasive species in that it includes a large range of anthropic variables [17], control of

most important biases [18] temporally independent evaluation [17, 19] and a robust approach

based on TSS and AUC statistics combined with comparisons to null models [20] (Fig 1).

Materials and methods

Study area and species

Islands provide good opportunities for studying invasion processes due to their isolation–here

we used Great Britain. We divided the study area into 5x5 Km2 grid cells but excluded those

with less than 70% of the grid area (typically, coastal ones), giving a total of 8,735 valid cells.

We used this grid resolution to avoid streams from different catchments being present in the

same grid and to retain as many presence/absence records as possible. Grid cells have been

previously used as reference area to study the distribution of freshwater species in broad areas

when using river fragment as reference is arbitrary and computationally tedious [13, 21, 22].

We modelled the distribution of nine species from five different taxa (fish, arthropods, mol-

luscs, amphibians and reptiles): the wels catfish (Silurus glanis), pumpkinseed (Lepomis gibbo-sus), zander (Sander lucioperca) and sunbleak (Leucaspius delineates) amongst the fish; signal

crayfish (Pacifastacus leniuscus), killer shrimp (Dikerogammarus villosus) amongst the arthro-

pods; the zebra mussel (Dreissena polymorpha) among the molluscs; the marsh frog

Improving Species Distribution Models of freshwater invaders

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Competing interests: The authors have declared

that no competing interests exist.

(Pelophylax ridibundus) amongst the amphibians, and the red-eared slider (Trachemys scripta)

among the reptiles. Species occurrence records in the invaded region were obtained from the

NBN Gateway database (http://www.nbn.org.uk/), which is the most complete source of non-

native species distribution data in Great Britain [23] and species occurrence in the native area

were obtained from the Global Biodiversity Information Facility (GBIF, http://gbif.org).

To account for sampling bias [24] we compared the distribution of the nine invasive study

species with the distribution of similar native species for each taxon. This comparison

accounted for the number of presence of native species in the absence of invasive species. The

purpose of this analysis was to make sure that grid cells included in our study had been sam-

pled for similar species, providing greater confidence on the absence of AIS [25, 26]. We used

data from the NBN database to compare the distribution of invasive fish in Great Britain with

those of brown trout (Salmo trutta), Atlantic salmon (Salmo salar), spined loach (Cobitis tae-nia), European bullhead (Cottus gobio) and Allis shad (Alosa alosa); we used the distribution

of the common frog (Rana temporaria) and the common toad (Bufo bufo) for amphibians, and

the distribution of 21 species of Gammarus was used as a control for the killer shrimp. We

could not find comparable data for the distribution of the red-eared slider, the zebra mussel

and the signal crayfish since there are no native sliders in Great Britain and the native freshwa-

ter pearl mussel (Margaritifera margaritifera) and the white-clawed crayfish (Austropotamo-bius pallipes) are critically endangered, or endangered, respectively, and their current

distributions would not be representative.

We used data from GBIF to compare the distribution in the native area of the pumpkinseed

with the largemouth bass (Micropterus salmoides) which is a well sampled species due to its

interest as a game species, the signal crayfish with the pilose crayfish (Pacifastacus gambelii)

Fig 1. Diagram of the Species Distribution Modelling procedure. Dashed boxes mark the parts of the approach that have been improved in our study as compared to

the common procedure.

https://doi.org/10.1371/journal.pone.0217896.g001

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the only native crayfish sharing distribution range [27], and the red eared slider with the south-

ern painted turtle (Chrysemys picta) and river cooter (Pseudemys concinna). Wels catfish,

sander and sunbleak were compared to barbel (Barbus barbus), northern pike (Esox lucius)and gudgeon (Gobio gobio).

Pseudo-absences and background data corresponded to those areas without invasive spe-

cies. We randomly selected pseudo-absences after checking the sampling effort, instead of

incorporating the sampling effort to the model because most invasive species had more than

70% of their area sampled; justified by the presence of at least another related species or lack of

sampling bias information [25, 26]. We also used this approach to avoid bias towards places

with a high number of occurrence records, as many invasive species might be introduced in

remote places where sampling is less common due to the accessibility [24].

As the spatial domain of the study area needs to be constrained in order to retain only

meaningful ecological variables [28], we excluded those cells that were 200 kilometres beyond

the northernmost presence for each species in the invaded area, and used a convex hull of

occurrences in the native area, to obtain a more representative environmental domain [29].

Modelling scenarios and predictor variables

Three different scenarios were used based on the inclusion of different types of predictors: (i)

environmental variables only in the invaded area (INVADED), (ii) environmental variables in

both the native and the invaded area (NATIVE) and (iii) environmental and anthropic vari-

ables in the invaded area (MIXED). Anthropogenic variables cannot be combined with the

native range since they usually have the contrary effect than in the invaded area since human

activities use to negatively impact native species distribution ranges [30]. We used 19 biocli-

matic variables, as well as altitude and slope as topographic variables, and land use as a proxy

for the fundamental niche [9, 31]. We extracted the mean values of the grid cells of all the vari-

ables (Table 1) in each grid cell using the zonal statistic tool in QGIS [32]. Using the hydrogra-

phy map, we estimated land use predictors within a 50 m buffer strip from each river bank.

In order to model human-mediated geographical range expansion (i.e. promoted by

anthropically mediated spread and/or propagule pressure), we included the distance to the

closest town and city (with more than 100,000 habitants), and population density as an indica-

tor of human presence and pressure. As an indicator of human accessibility, we used road den-

sity, distance to the nearest port, and distance to the nearest boat launch ramp. We also

included density of reservoirs, lakes, and canals as an indicator of building infrastructures and

places that may facilitate the spread and/or arrival of AIS through human activities like

angling, canoeing or boating [34]. Aquaculture facilities, garden centres and pet stores have

been reported to be sources of introduction and dispersal of AIS [35]. For that reason, we

included the distance to these three types of facilities to account for potential sources of intro-

duction and propagule pressure. All proximity variables (e.g., distance to boat launch ramp or

to pet stores) were calculated by creating a distance map in QGIS and then extracting the

mean values for each grid cell. All models using the invaded area included the Euclidean dis-

tance to the first record of introduction to account for spatially-correlated patterns of dispersal,

as this approach has previously been shown to perform better than more complex SDMs mod-

els [36, 37]. We accounted for collinearity by calculating the Variance Inflation Factor [VIF

[38], based on the R-squared value of the regression of one variable against all other variables

and defined as VIF_j = 1/(1-R_j^2),. Twelve bioclimatic variables were excluded due to multi-

collinearity (VIF > 10; see Table 1), retaining 23 variables for modelling [39]. For each sce-

nario and species, the distribution was analysed using five independent SDMs algorithms:

Generalised Additive Models [GAM [40]] using the mgcv package in R [41] and MaxEnt [42]

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Table 1. Predictor variables used to generate the Species Distribution Models. Variables in bold had VIF scores smaller than 10 [33] and were included in the Species

Distribution Models.

Predictor Variable Source Description

Distance to the first

record

https://data.nbn.org.uk/ and http://www.nonnativespecies.org/

factsheet/

Euclidean distance from the first record

reported in the database and in accordance

with each species factsheet.

ENVIRONMENTAL

Slope http://www.sharegeo.ac.uk/handle/10672/7 Mean slope in each grid obtained from a

Digital Elevation Model

Altitude http://www.sharegeo.ac.uk/handle/10672/5 Mean slope in each grid obtained from a

Digital Elevation Model

Climatic Bio1 http://www.worldclim.org/bioclim Annual Mean Temperature

Climatic Bio 2 http://www.worldclim.org/bioclim Mean Diurnal Range (Mean of monthly (max

temp—min temp))

Climatic Bio 3 http://www.worldclim.org/bioclim Isothermality (BIO2/BIO7) (� 100)

Climatic Bio 4 http://www.worldclim.org/bioclim Temperature Seasonality (standard deviation�100)

Climatic Bio 5 http://www.worldclim.org/bioclim Max Temperature of Warmest Month

Climatic Bio 6 http://www.worldclim.org/bioclim Min Temperature of Coldest Month

Climatic Bio 7 http://www.worldclim.org/bioclim Temperature Annual Range (BIO5-BIO6)

Climatic Bio 8 http://www.worldclim.org/bioclim Mean Temperature of Wettest Quarter

Climatic Bio 9 http://www.worldclim.org/bioclim Mean Temperature of Driest Quarter

Climatic Bio 10 http://www.worldclim.org/bioclim Mean Temperature of Warmest Quarter

Climatic Bio 11 http://www.worldclim.org/bioclim Mean Temperature of Coldest Quarter

Climatic Bio 12 http://www.worldclim.org/bioclim Annual Precipitation

Climatic Bio 13 http://www.worldclim.org/bioclim Precipitation of Wettest Month

Climatic Bio 14 http://www.worldclim.org/bioclim Precipitation of Driest Month

Climatic Bio 15 http://www.worldclim.org/bioclim Precipitation Seasonality (Coefficient of

Variation)

Climatic Bio 16 http://www.worldclim.org/bioclim Precipitation of Wettest Quarter

Climatic Bio 17 http://www.worldclim.org/bioclim Precipitation of Driest Quarter

Climatic Bio 18 http://www.worldclim.org/bioclim Precipitation of Warmest Quarter

Climatic Bio 19 http://www.worldclim.org/bioclim Precipitation of Coldest Quarter

Land Uses: Grasslands

in the riverside

CORINE Land Cover

http://land.copernicus.eu/pan-european and North American

Land Cover Monitoring System (NALCMS) http://www.cec.org/

tools-and-resources/map-files/land-cover-2010-landsat-30m

Percentage of grassland and cropland in a 100

m buffer along the river

Land Uses: Natural

forest in the riverside

Percentage of preserved forest in a 100 m

buffer along the river

ANTHROPIC

Lakes/ Reservoir https://www.sharegeo.ac.uk/ Percentage of lakes and/or reservoirs

Distance to

cities > 100K

population

Own creation based on data from Office of National Statistics Euclidean distance to human settlements with

more than 100000 inhabitants based on 2011

census

Population density Diva-GIS http://www.diva-gis.org/Data Population density

Distance to pet stores Own creation Average Euclidean distance to the closest pet

stores

Distance to garden

centers

Own creation Average Euclidean distance to the closest

garden centres

Distance to farms Own creation Average Euclidean distance to the closest

aquaculture facility, farm or hatchery

Road density https://www.ordnancesurvey.co.uk/ Kilometres of road

Distance to Boat

Launch

http://www.boatlaunch.co.uk/#/map Euclidean distance to the closest freshwater

boat launch

Distance to Ports https://www.sharegeo.ac.uk/ Euclidean distance to the closest port

Canal density https://www.sharegeo.ac.uk/ Meters of river channels

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using the dismo package [43], Boosted Regression Trees [BRT [44]], Generalized Linear Mod-

els [GLM [45]] and Random Forest models [RF [46]]; and an ensemble model including all

these algorithms. For this, we used biomod2 package in R [47] and the ensemble was calculated

by averaging model predictions weighted by ROC and TSS. We included single algorithms

and ensemble to minimise the uncertainty of the techniques selection and outputs[48].

Training and testing data

We divided the presence data on the invaded region into training and testing data sets for each

species based on the date the species were first reported in a given locality. This approach is

more robust than randomly selecting training and testing presence data [19, 49, 50]. It also

allows the evaluation of each model using a temporally independent validation to recreate the

invasion process followed by the species and investigate if the patterns detected by the models

at time 1 are similar at time 2[37, 51, 52]. We selected the 70% oldest records for training and

the remaining 30% of records (i.e. most recent) for testing. For the NATIVE models, we

included all the presence records available in the native region in addition to the 70% of rec-

ords of the invaded region to account for whole range of conditions where the species are able

to persist [53]. For training pseudo-absences, we randomly chose the same number of grid

cells as the presence for each species to minimize the potential effect of prevalence. Testing

pseudo-absences were selected based on the correction for sorting bias (see below).

Spatial sorting bias may pose a problem due to spatial autocorrelation and tends to generate

inflated model results [54]. We removed this bias by pairwise distance sampling implemented

in the dismo package in R [43].

Model performance was assessed using True Skills Statistic [TSS [55]] and the Area Under

the Curve [AUC, [56]] measures of accuracy. Although the idea that SDMs perform better

than random when AUC is> 0.5 [57] and/or TSS is> 0 [55] is widespread, this makes the

implicit assumption that there is no spatial sorting bias in the evaluation data. For this reason,

we built null models to assess whether the performance of the SDMs for each species, algo-

rithms/ensemble and scenario was better than expected by chance. This is a suggested

approach when using pseudo-absences that allows for significance testing of SDMs [20]. Null

model can be based on randomizations of ecological data or random sampling from a distribu-

tion [58]. In our study, the null models (i.e. those expected by chance alone) were created

using the same training and testing distribution data used for the real models but with ran-

domly reshuffled predictors. For each species, algorithms/ensemble and scenario we obtained

1000 null models, each one with different rearrangement of the predictors [20, 59] obtained by

permutation using base R [60]. We then run 1,000 permutations for each model, and as for the

real models, we then calculated performance statistics as above.

In order to extract the distribution of performance statistics (i.e. TSS and AUC) for the null

models (thereafter TSSnull and AUCnull), we assessed the upper limit of the 95 confidence

interval by calculating the 97.5 percentile in the distribution of the 1,000 performance statistics

generated for each null model. Then, we calculated the differences in the accuracy measures

between the null model and the real model by subtracting the real model statistic value by the

null model statistic value (thereafter ‘effect size’, AUCes and TSSes). Hence, positive values

indicate that the model performed better than null models, whereas negative values indicate

that the model performed worse than null models (i.e. no better than random).

We obtained the best model for the nine species for each of the five different algorithms

(GAM, MaxEnt, BRT, RF and GLM) and the ensemble model, and the two values of SDM per-

formance (i.e., TSSes and AUCes) to determine which overall scenario (i.e. Native, Invaded or

Mixed) predicted the species distribution best. To analyse the importance of scenario,

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algorithm and, the characteristics of the species’ records and species invasion (see Table 2) in

the performance, we used the values of all the models better than null and employed linear

mixed models (LMM) for each performance metrics (AUCes and TSSes) considering species

as random factor.

Regarding the characteristics of the species, we considered that the ‘time since introduc-

tion’, the number of localities occupied by the species (i.e., ‘number of records’) and the ‘dis-

tance between the northernmost and southernmost occurrences’ were indicators of the

available time for adaptation or species ability to cope with new conditions, potentially affect-

ing model performance. Likewise, proximity between native and invaded region (i.e., ‘native

region’) could indicate similarity of conditions whereas ‘economic interest’ might favour the

species to be present in particular localities (e.g., recreational areas) which might be easy to

predict. Species characteristics were extracted from the factsheet published by GB Non-native

Species Information Portal (www.nonnativespecies.org/factsheet/) and the spatial records

characteristics were obtained from the species distributions using QGIS. We assessed LMM

assumptions by checking residual plots, normality of residuals, and plots of scaled residuals

versus fitted values. No significant deviations from linearity or normality were found nor obvi-

ous outliers. All analyses were conducted in R 3.3.1 [61].

Results

Between 71% and 72% of the grid cells with watercourses in Great Britain included at least one

record of a native species of the amphibian and fish groups, respectively. In the native area of

the different species between a 69% and a 95% of the grids were sampled for at least a related

species.

All TSS for the real models (TSSreal) values but six were higher than 0, and all but 16

AUCreal values were higher than 0.5. The average and standard deviation value for the TSS and

AUC performance statistics from the real models were 0.25 ± 0.15 and 0.60 ± 0.11 respectively

(S1 Table). TSSnull values averaged 0.36±0.24 and AUCnull values averaged 0.68±0.13. The spe-

cies with best average results was the red-eared slider with average of TSS and AUC of 0.66

and 0.28, respectively. The species with highest values of performance in the null models was

the killer shrimp with average of TSSnull and AUCnull of 0.67 and 0.86, respectively. (S1

Table). The best performance values for the effect size were for the sunbleak according to the

AUCes (0.078) and the TSSes (0.25).

The null model approach indicated that models performed better than chance for seven of

the nine AIS: signal crayfish, zebra mussel, red-eared slider, zander, wels catfish, marsh frog

and sunbleak (S1 Table). Importantly, this approach showed that relying on a given TSS or

Table 2. Characteristics of the species’ spatial records and their invasion used as predictors to model the overall performance ability of the freshwater invasive Spe-

cies Distribution Models.

Species Time since Introduction (yrs.) Economic interest No. presences Distance between N-S occurrences (km.)

Zebra mussel 191 No 376 398

Red-eared slider 60 Yes 87 406

Marsh frog 133 No 66 230

Pumpkinseed 97 No 20 486

Zander 138 Yes 115 172

Killer shrimp 6 No 8 90

Signal crayfish 40 Yes 544 506

Sunbleak 21 No 18 182

Wels catfish 152 Yes 94 250

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AUC value is not sufficient to conclude that a model is reliable since the same or similar accu-

racy measures’ values (AUC and TSS) for the real models were both better and worse than

chance according to the null models (S1 Table). For instance, AUC values of 0.58 (Signal cray-

fish Ensemble Native model) were better than chance according to the null models (0.03

whereas AUC values of 0.7 (Red-eared slider GAM Invaded) or 0.73 (Pumpkinseed GAM

Invaded) were worse than null models (S1 Table). Similarly, relying only on a single perfor-

mance statistic or a single modelling algorithm can mask model uncertainty. Specifically, 26

out of the total of 135 fitted models (19.3%) performed better than expected by chance accord-

ing to both performance statistics (i.e. TSSes and AUCes), whereas if only one performance

statistic is considered (i.e. TSSes or AUCes), the number of valid models increased to 39 (29%)

(S1 Table). For example, for the wels catfish, the Mixed and Invaded Scenarios with Maxent

performed better than the null model (all AUCes and TSSes = 0.03) whereas using Ensemble

or GLM modelling, only the Invaded Scenario was better than chance and only according to

one of the effect sizes (TSSes for Ensemble = 0.08 and AUCes for GLM = 0.003), and no GAM

and RF models did better than chance. For marsh frog, Mixed MaxEnt, Native GAM and

Mixed and Native for RF performed better than expected by chance, whereas no Ensemble or

GLM models for this species performed better than the null models. We were unable to obtain

results for the BRT null models because the algorithm did not converge. Therefore, this algo-

rithm was only considered as part of the ensemble.

Null models performed best in 55% of the cases followed by the Mixed scenario (29%),

Native scenario (7%) and Invaded (7%) (Fig 2). According to the Wald test, scenario was a sig-

nificant predictor of the TSSes (Table 3) and in the LMM the Native Scenario had a negative

relationship (estimate = -0.032, sd = 0.01, p<0.01) and Mixed Scenario had a positive relation-

ship (estimate = 0.1, sd = 0.03, p<0.05) with the TSSes. Algorithm and Time since introduc-

tion had also a marginally significant relationship with the TSSes (Table 3). None of the

considered predictors had an effect on the AUC effect size (Table 3). Least square means and

Fig 2. Summary of the best model scenario for the nine invasive species under study according to the three

different algorithms/ensemble and the two statistics (i.e. TSS and AUC). ‘Invaded’ scenario included environmental

predictors from invaded regions, ‘Native’ included environmental predictors from both native and invaded regions

and ‘Mixed’ scenario included environmental and anthropogenic from the invaded region. When two scenario

obtained same values another category was created with the ‘ = ‘ symbol to illustrate it.

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their confidence intervals from the AUCes and TSSes mixed models illustrated the differences

in performance for the different algorithms over the different scenarios (Fig 3).

Discussion

We have shown that both environmental (from the native and invaded ranges) and anthropic

variables should be included in models that aim to understand and predict the distribution of

aquatic invasive species. Our results also highlight the fact that different species may require

different sets of predictors and that the inclusion of information about conditions in the spe-

cies’ native area may be required to model their distribution accurately, making it difficult to

generalize across taxa. Therefore, including as much information in the models as possible will

help to find the model with the best predictive ability for the species under study, and will per-

mit comparisons between different modelling approaches, as it is not possible to know a prioriwhich ones might work best, in agreement with the justification of using ensemble modelling

approaches [48].

When the aim is to forecast species’ distributions for management purposes, it has been

suggested that the inclusion of anthropogenic variables is essential [16, 62]. For example,

human-mediated dispersal may be the only reason for the rapid spread of invasive plants [63],

Fig 3. Meanvalues of AUCes and TSSes for the five algorithms with results and the three scenarios. Boxes indicate

the least square means based on a linear mixed models considering Scenario and Algorithm. Error bars indicate the

95% confidence interval of the least square means.

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Table 3. Results from Wald test of the linear mixed models applied to analyse the relationship between model performance (measured by TSSes and AUCes effect

size values) and the type of scenario, algorithm, their interaction and species’ characteristics.

AUCes TSSes

Predictor Chisq df p-value Chisq df p-value

Scenario 3.9904 3 0.263 12.2460 3 0.007

Algorithm 3.5642 4 0.468 9.2427 4 0.055

Scenario:Algorithm 7.9929 7 0.333 1.0903 6 0.982

Distance between northernmost and southernmost records 0.0313 1 0.860 0.3420 1 0.559

Number of presences 0.4068 1 0.524 0.0026 1 0.959

Economic interest = YES 0.1582 1 0.691 1.5679 1 0.211

Time since Introduction 0.0198 1 0.888 3.6201 1 0.057

https://doi.org/10.1371/journal.pone.0217896.t003

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stressing the need to consider a variety of predictors. In practice, many management and con-

servation plans rely on models that forecast species distributions based only on climatic vari-

ables [64], which, according to our study, might result in less effective management of some

AIS if resources are invested in addressing the wrong type of drivers. Certainly, models that

only use climatic variables are useful to delimit management actions to suitable regions where

the species are potentially able to spread without human intervention (i.e., fundamental niche

[65]). However, for many species, projecting the distribution of invasive species onto future

scenarios of climate change to forecast species expansion will benefit from the integration of

anthropogenic variables [16] because human-mediated range-shifts might be more intense

than shifts due to climate change [11].

Regarding model performance, our SDMs did not explain the distribution better than

chance for two of the nine freshwater invasive species according to the null models. This high-

lights the difficulties of understanding invasion patterns for some species [66]. Also, the effect

sizes (TSSes and AUCes) were low for the better than null models which might be a result of

our more robust evaluation of predictive ability, as we accounted for sorting bias and tested

the models with a real time independent evaluation.

However, seven species obtained models that performed better than chance even with our

robust evaluation procedure, supporting the validity of using SDMs in invasion biology with

the right set of predictor variables and algorithms.

AUC and TSS are some of the most commonly used statistics for measuring model accu-

racy of correlative species distribution models [67]. However, according to our results perfor-

mance needs to be further assessed, for example, by comparison to null models [59]. AUC

validity has been criticised before [68, 69] and although the use of null models for SDMs had

been previously recommended [20, 70], this approach has not yet been widely adopted.

None of the characteristics of the species had a significant effect on the performance. How-

ever, time since the first introduction was marginally significant for one of the performance

metrics (Table 3) so we considered inappropriate to rule out their effects on performance. Pre-

vious studies indicated that the characteristics of the species distribution patterns affected the

accuracy of SDMs [71]. Time since the first introduction is important for species to adapt and

reach suitable areas, making it difficult to discriminate between occupied and unoccupied

localities [72]. Newly arrived species typically have small range sizes and, as it has been

reported previously [73], modelling species with small number of occurrences or restricted

range size requires caution and special protocols particularly in the early stages of invasion,

when data limitations make SDMs less accurate [74].

Our study is the first attempt to model freshwater invasions including detailed information

from both native and invaded regions and also on anthropic and propagule pressure of differ-

ent taxa in a relatively isolated system, accounting for bias in the SDMs to avoid overfitting

[18]. Our models did not explain the distribution of killer shrimp and pumpkinseed and for

other species the predictive performance was low which might be due to the lack of consider-

ation of biological interactions which is one of the factors governing species’ distributions

[65]. The use of mechanistic models might further improve our understanding of AIS dispersal

[75] by detecting niche shifts during invasion [76]. Given that the number of invasive species

continues to increase [77], there is an urgent need to improve predictive management methods

since most countries still lack the ability to control invasive species effectively [78].

In conclusion, our study suggests the use of null models to assess model performance will

help gain a better understanding of macroecological processes in invasion biology, because

relying only on AUC and TSS or a single modelling algorithm is insufficient to obtain reliable

models for management. Forecasting invasive species distribution under future scenarios of

climate change will be more realistic for a higher number of species if a combination of

Improving Species Distribution Models of freshwater invaders

PLOS ONE | https://doi.org/10.1371/journal.pone.0217896 June 17, 2019 10 / 14

bioclimatic and anthropogenic variables is considered. Finally, our results also indicate that

the distribution of freshwater species with restricted number of records, with higher distances

between northernmost and southernmost records and that lack economic interest are particu-

larly difficult to predict, and should therefore be a research priority.

Supporting information

S1 Table. True Skill Statistic (TSS) and Area Under the Curve (AUC) results for real and

null models for eleven species, two algorithms and the ensemble, and three scenarios.

Effect size corresponds to the difference between the real model and the highest 95CI values of

both discrimination statistics.

(DOCX)

Author Contributions

Conceptualization: Marta Rodrıguez-Rey, Carlos Garcia de Leaniz.

Data curation: Marta Rodrıguez-Rey.

Formal analysis: Marta Rodrıguez-Rey.

Funding acquisition: Sofia Consuegra.

Methodology: Marta Rodrıguez-Rey, Sofia Consuegra, Luca Borger, Carlos Garcia de Leaniz.

Project administration: Sofia Consuegra.

Supervision: Sofia Consuegra, Luca Borger, Carlos Garcia de Leaniz.

Visualization: Marta Rodrıguez-Rey.

Writing – original draft: Marta Rodrıguez-Rey.

Writing – review & editing: Marta Rodrıguez-Rey, Sofia Consuegra, Luca Borger, Carlos Gar-

cia de Leaniz.

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